Pythagorean Theorem (1)

For the right triangle marked in green (on the left), the size of the legs (catheti) can be varied by the two sliders.

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Let a and b be the lengths of the legs in the given right triangle (green, on the left). The question is how the length of the hypotenuse (c) depends on a and b. In the right part of the drawing area two squares with side length a + b are shown. In both squares four triangles (green) are drawn, which are congruent to the given triangle. The remaining area consists in one case (drawing top right) of the squares on the legs (blue and red), in the other case (drawing bottom right) of the square on the hypotenuse (violet).

Pythagorean theorem:
In a right triangle, the sum of the squares of the two legs (catheti) is equal to the square of the hypotenuse.
a2 + b2 = c2

Another way to proof the Pythagorean theorem is demonstrated here.